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Standing Wave and SWR

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Standing Wave and SWR Standing Wave and SWR Standing Wave and SWR SWR or Standing Wave Ratio is one of the most misunderstood terms in amateur radio. Even though every antenna and transmission line book that I have seen, is quick to point that out, it still is the source of many misconceptions. To most hams with an SWR meter, SWR is whatever the meter reads and if the meter says there's no problem, (SWR is low enough) then the antenna is well. That simply isn't true. So, I will once again explain what exactly SWR is and isn't. First of all, SWR is not an antenna property or a characteristic. SWR is a measure of an antenna system. An antenna system consists at least of two parts: the antenna itself and the feedline from the antenna to the transceiver. Additionally, the antenna system may include, transformers, baluns, matching devices such as an Antenna Tuning Unit, (ATU) etc. When a wave traveling along a transmission line (with characteristic impedance Zo) from the transmitter to the antenna (incident wave) encounters an impedance (Za = Ra ±jXa), that is not the same as Zo then some of the wave energy is reflected (reflected wave) back toward the transmitter. Whenever two waves of the same frequency propagate in opposite directions along the same transmission line, as occurs in any system exhibiting reflections, a static interference pattern (standing wave) is formed along the line. In the best circumstances, we would use a 50-Ohm transmission line to connect a 50-Ohm impedance antenna to a transmitter rated at 50-Ohm output impedance. In that case, everything is matched and as long as we make sure there are no currents flowing on the coax shield, everything should work great. Since all parts of the system are matched, transmission line losses are minimized, the transmitter can operate at its designed efficiency and almost all of the power output by the transmitter will get to the antenna and be radiated. For the purposes of quantifying reflection magnitude, we are interested in the amplitude of the voltage or the current maxima and minima. The SWR is defined as the ratio of the voltage or the current maximum to the voltage or current minimum along a transmission line as follows: SWR = Vmax / Vmin = Imax / Imin SWR can be measured using either a current or voltage sensor as it is moved along the transmission line while comparing the maximum with the minimum. SWR is always greater than or equal to one. If no reflections exist, no standing wave pattern exists along the line and the voltage or current values measured at all points along the transmission line are equal. In this case, the impedance match is perfect and the SWR equals unity. The most and convenient method to measure the SWR is using a reflectometer. This instrument comprises two power meters, one reading the incident power and the other the reflected power. Power detector directivity is possible because the incident wave voltage and current are in phase and the reflected wave is 180º out of phase. What is SWR really? SWR is one way to register the mismatch between the ultimate load and the transmission line characteristic impedance. SWR is a measure of what conditions exist on the transmission line. Those conditions exist all along the transmission line with a little allowance for some line losses. SWR is not a measure of how well the antenna works. Low or high numbers can occur for antennas with identical far field patterns operating with essentially the same efficiency. As example: a half-wave dipole with 75-ohm resonance impedance, either fed with a coax of 50- or a 450-ohm window ladder line, will have different SWR along the transmission line; respectively 1.5 for the 50-ohm coax line and 6 for the window ladder line. But the performance of both © ON5AU 2019 Page 1 Standing Wave and SWR dipoles will be practically the same when both antenna systems are properly matched to the transmitter’s 50-ohm output impedance. I want to clear up one common misconception and that is why as said above: resonance impedance (= only resistive). SWR is not simply the ratio of the antenna impedance (Za) to the Zo of the transmission line. The antenna impedance is nearly always a complex value having not only resistance but also reactance either capacitance or inductance (jX). Consider the following antenna impedances presented to a 50-ohm coaxial cable in Table 11.1. Za Zo SWR 50 jX 0 50 1 75 jX 0 50 1.5 100 jX 0 50 2 50 jX 50 50 2.62 75 jX 50 50 2.42 100 jX 50 50 2.62 Table 11.1. SWR with different antenna impedances (Za) and equal transmission line impedance (Zo) either without reactance (jX 0) or with reactance (jX 50) . To illustrate standing wave, I modeled a 300-ohm feedline, [11-3.EZ]. The source is at the left and the load at the right, Figure 11.4. I considered four different antenna loads and two power levels: • Case A. The antenna load impedance equals exactly the characteristic impedance of the transmission line Za = Zo = 300 ohms and is purely resistive. If we should measure the voltage or the current at any point along the transmission line, they should be the same. No reflected wave should be noticed and the SWR shall be 1:1. • Case B. The antenna load impedance is twice the characteristic impedance of the transmission line Za = (Zo X 2) = 600 ohms and again purely resistive. If we should measure the voltage or the current at any point along the transmission line, they should differ. We should find points of maximum and minimum voltage and current. This indicates the existence of a standing wave. When we divide the maximum voltage or maximum current by the minimum voltage or minimum current we should have a ratio of 2:1 being the SWR. • Case C. The antenna load impedance is twice the characteristic impedance of the transmission line but has also a reactance of jX 300 ohms. The complex antenna impedance is now 600 jX 300 ohms. If we should measure the voltage or the current at any point along the transmission line they should also differ. We should find also points of maximum and minimum voltages and current but they should differ from case B with no complex impedance. Here also, the existence of a standing wave. When we divide the maximum voltage or maximum current by the minimum voltage or minimum current, we should have a ratio of 2.58:1 as being the SWR. • Case D. The antenna load impedance is five times the characteristic impedance of the transmission line but has also a reactance of jX 300 ohms. The complex antenna impedance is now 1 500 jX 300 ohms. If we should measure the voltage or the current at any point along the transmission line, they should again differ. Here also is the existence of a standing wave. When we divide the maximum voltage or maximum current by the minimum voltage or minimum current we should have a ratio of 5.05:1 as being the SWR. © ON5AU 2019 Page 2 Standing Wave and SWR The current plots of the four above models are found at Figure 11.4 and the computed voltage, current and SWR at Table 11.2. When the SWR becomes rather high then the current and voltage can become extremely high in special with high power. That’s why transceivers as precaution, reduce the output power when it encounters high SWR. The high current or voltage could when to high, destroy transceiver output components. Also, caution should be taken in the choice of the transmission line to withstand the high voltage. Figure 11.4. The current along a modeled transmission line with various antenna load impedances Load Power Minimum Maximum Maximum Minimum SWR Current Voltage Current Voltage Ohm Watt Ampere Volt Ampere Volt Ratio 300 jX 0 100 0.58 173 0.58 173 1:1 300 jX 0 1 000 1.82 548 1.82 548 1:1 600 jX 0 100 0.41 244 0.82 122 2:1 600 jX 0 1 000 1.3 771 2.59 385 2:1 600 jX 300 100 0.4 273 1.05 106 2.58:1 600 jX 300 1 000 1.28 862 3.3 334 2.58:1 1 500 jX 300 100 0.26 389 1.3 78 5.05:1 1 550 jX 300 1 000 0.82 1 230 4.1 244 5.05:1 Table 11.2. The maximum/minimum voltage and current, and the SWR obtained along a modeled feedline of 300 ohms with various load values and a power of 100 and 1000 watts. A mismatch between the antenna impedance, the transmission line characteristic impedance and the transmitter output impedance always leads to a standing wave and a certain SWR. Having an SWR in your antenna system is inevitable. First, having an antenna with a load impedance equal to the characteristic transmission line impedance is not always achievable. The choice of different feedline impedances is not to great Second, the lowest SWR is at the resonant frequency and will always increase when working more toward the frequency band edges. So, the magic 1:1 SWR (for most hams) is hard to obtain. © ON5AU 2019 Page 3 Standing Wave and SWR Having SWR in your antenna system leads to extra power losses. But even so, is having the lowest possible SWR always a concern to pursue? Ham radio has its share of misinformation, misconceptions and misunderstandings among its participants.
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